If it makes you feel any better, after trying several methods I did the exact same thing, used a hose removal pick tool like what you have, with the curved tip, to dig out the residue. Just be sure to rotate it 180-degrees to scrape deeply along both sides to get every little bit out or you will have a very hard time getting the new stuff in. You could also try heating with a heat gun or hair dryer bit by bit to see if that makes it easier to remove, but it may be easier when it's cold and the parts break out in larger pieces. I didn't use the heat method as nothing was available to me at the time. I wonder if penetrating fluid would help release it from the channel a bit? Maybe not worth the cleanup or risk of handling a slippery piece of rare and expensive glass.